How to set the origin point of each bone differently?
OK, There is only one object origin because it's the origin of your object. It's the 0,0,0 point of reference for all bones inside the armature. All bones share this one origin. It's the ball joint that connects the invisible shoebox with the outside world. In that invisible shoebox lies the armature.

In Object Mode, the whole armature rotates around this.

In Pose Mode, every bone usually rotates around it's own root unless constrained in some way.

You are in Edit Mode where neither necessarily applies. There, stuff rotates around the pivot point. That can be, for example, the center of your selection or, if chosen: the 3D Cursor. It changes violently depending on your settings and your selection.



That also means you are often not merely rotating, you are rotating and moving bones.

Example: you select an entire bone (orange, Edit Mode) and it rotates around its middle. That's not a rotation, that's moving its tip and root in a circular motion. Tip and root will have changed their coordinates.

You select an entire bone (blue, Pose Mode) and it rotates around its root. This is a true rotation because only the direction in which the bone points has changed. 

Tip: use CTRLF3 with 'Fullscreen' disabled to make screenshots. Without the header or the properties (N) it's hard to see what you are doing.

I think learning by doing is beginning to reach its limits for you. Flying blind can be tiring. You will run into lots of roadblocks if you keep using Blender without knowing it's fundamental concepts of how it organises its data and its hierarchies.

Make it a sport to read a few pages of documentation every day. Otherwise you keep having blind spots creeping up on you when you need it the least ( :